Date/Time : 28 Nov 2025 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Koulik Khamaru, Rutgers University

Modern decision-making increasingly relies on adaptive experimentation, particularly in settings such as A/B testing, multi-armed bandits, and reinforcement learning. While these methods enable more efficient learning and allocation of resources, they fundamentally challenge traditional statistical inference. Classical i.i.d.-based tools often break down under adaptive data collection, resulting in biased estimators and misleading confidence intervals.

This talk offers an overview of statistical inference in these adaptive environments. We highlight the pitfalls of naive inference through concrete examples and introduce the concept of stability—originally formulated by Lai and Wei (1982)—as a unifying principle for valid inference under adaptivity. A key advantage of stability is that it allows us to recover classical inferential guarantees—such as asymptotic normality and valid confidence intervals—even when the data arise from highly adaptive algorithms. In other words, stability serves as the bridge that lets i.i.d.-based tools remain valid in non-i.i.d. bandit settings.

Next, we discuss the stability properties of two widely used algorithms: the Upper Confidence Bound (UCB) and Thompson Sampling. We argue that while UCB is stable, Thompson Sampling is not. Finally, we propose a modification of Thompson Sampling that regains stability while maintaining near-optimal regret. Key illustrations include quantitative central limit theorems of empirical mean in stochastic bandits and least square estimators in contextual bandits. We also present a new proof technique for analyzing regret and establishing stability, which we believe has broader applicability and may be of independent interest.

The talk is based on a series of joint works with Cunhui Zhang, Qiyang Han, Budhaditya Halder, Subhayan Pan, and Samya Praharaj.

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Date/Time : 21 Nov 2025 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Seonwoo Kim, Yonsei University

The main purpose of this lecture course is to introduce the recently-developed resolvent approach [Landim-Marcondes-Seo, JEMS ’25] to metastability and beyond. First, I will review the historical developments in the treatment of the metastability phenomenon and summarize the pros/cons of the previous methods. Next, I will state and prove the resolvent approach in a simple setting, focusing especially on its strength, along with some real-model applications. Finally, I will summarize my recent work with Jungkyoung Lee (KIAS) to extend and generalize this approach to non-compact metastable transitions.

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Date/Time : 19 Nov 2025 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Seonwoo Kim, Yonsei University

The main purpose of this lecture course is to introduce the recently-developed resolvent approach [Landim-Marcondes-Seo, JEMS ’25] to metastability and beyond. First, I will review the historical developments in the treatment of the metastability phenomenon and summarize the pros/cons of the previous methods. Next, I will state and prove the resolvent approach in a simple setting, focusing especially on its strength, along with some real-model applications. Finally, I will summarize my recent work with Jungkyoung Lee (KIAS) to extend and generalize this approach to non-compact metastable transitions.

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Date/Time : 17 Nov 2025 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Seonwoo Kim, Yonsei University

The main purpose of this lecture course is to introduce the recently-developed resolvent approach [Landim-Marcondes-Seo, JEMS ’25] to metastability and beyond. First, I will review the historical developments in the treatment of the metastability phenomenon and summarize the pros/cons of the previous methods. Next, I will state and prove the resolvent approach in a simple setting, focusing especially on its strength, along with some real-model applications. Finally, I will summarize my recent work with Jungkyoung Lee (KIAS) to extend and generalize this approach to non-compact metastable transitions.

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Date/Time : 29 Oct 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Janosch Ortmann, University of Quebec in Montreal

The probabilistic coupling approach to study stochastic planar models originated in the works of Cator and Groeneboom on Hammersley’s process and the Poisson last-passage percolation (LPP). It has since been developed to treat many aspects of the KPZ universality in various models of directed LPP, directed polymers and interacting particles.

In this talk I will discuss two variants of the exponential LPP model: the bulk model, where the last-passage environment is given by independent Exp(1)-distributed weights on the integer quadrant and the (two-sided) boundary model, where an additional layer of independent Exp(w)-distributed weights are placed on the horizontal boundary and independent Exp(1-z)-distributed weights on the vertical boundary, for $0<w,z<1$. A particular interest for the increment-stationary case ($w=z$) arises from the fact that then the distribution of the LPP increments is invariant under lattice shifts.

I will discuss how the coupling framework can be used to derive optimal-order upper and lower bounds on the central moment for these two variants of exponential LPP. That is, letting $v$ be the LPP end-point we obtain bounds proportional to $\|v\|^{p/2}$ (CLT scaling) when $v$ is close to the axis and to $\|v\|^{p/3}$ (KPZ regime) otherwise. These bounds are also uniform over vertices taking values in these regions.

The talk is based on joint work with Elnur Emrah and Nicos Georgiou.

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Date/Time : 23 Oct 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Roberto Imbuzeiro Oliveira , Instituto Nacional de Matemática Pura e Aplicada (IMPA)

Estimating the mean of a random vector from i.i.d. data has received considerable attention. When the data take values in more general metric spaces, an appropriate extension of the notion of the mean is the Fréchet mean. While asymptotic properties of the most natural Fréchet mean estimator (the empirical Fréchet mean) have been
thoroughly researched, non-asymptotic performance bounds have only been studied recently.

This talk considers the performance of estimators of the Fréchet mean in general metric spaces under possibly heavy-tailed and contaminated data. In such cases, the empirical Fréchet mean is a poor estimator. We propose a general estimator based on high-dimensional extensions of trimmed means and prove general performance bounds. Unlike all previously established bounds, ours generalize the optimal bounds known for Euclidean data. Much like in the Euclidean case, the optimal accuracy is governed by two “variance” terms: a “global variance” term that is independent of the prescribed confidence, and a potentially much smaller, confidence-dependent “local variance” term. We apply our results for metric spaces with curvature bounded from below, such as Wasserstein spaces, and for uniformly convex Banach spaces.

The talk is based on arXiv:2509.13606, which is joint work with Daniel Bartl (NUS), Gabor Lugosi (ICREA/UPF), and Zoraida Rico (Bocconi).

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Date/Time : 15 Oct 2025 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Milind Hegde , Nanyang Technological University

A recurring theme in probability theory is that of universality: when extremely different looking systems have the same large scale statistical behavior. In the last few decades, an important new universality class has been discovered, called the Kardar-Parisi-Zhang (KPZ) universality class. However, the universality is only putative as only a handful of “metric” type models have been shown to lie in it in the strongest sense.

In this talk we will discuss a recent proof of membership in the KPZ class of the first non-metric type of model, namely the colored stochastic six-vertex model. The model arises naturally in probability theory and has connections to many areas of statistical physics and quantum integrable systems; e.g., the first form of the six-vertex model was introduced by Pauling in 1935 to model the crystal structure of ice. The Yang-Baxter equation and line ensembles (collections of random non-intersecting curves) will play fundamental roles in our discussion, but no prior background will be assumed. This is based on joint work with Amol Aggarwal and Ivan Corwin.

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Date/Time : 01 Oct 2025 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Akshay Hegde , National University of Singapore

Analysing the critical point structure of smooth Gaussian fields on $\mathbb{R}^d$ has been paramount in various probability problems. For example, the excursion probability P( sup f >u) can be precisely estimated by counting the number of critical points above the level u. Other examples include optimization of spherical spin glass models, percolation of level sets of smooth Gaussian fields. In this talk, we’ll explore the Poisson structure of high critical points of stationary smooth Gaussian fields. This is joint work with Dmitry Belyaev. 

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Date/Time : 19 Sep 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Giulio Ruzza, University of Lisbon

Random matrix theory is a central field in Mathematical Physics, linking probability, physics, number theory, and combinatorics. A main theme is Universality: the fact that, at large size, eigenvalue statistics look the same across many different models and even show up in distant areas such as random growth processes, random tilings, and the zeros of the Riemann zeta function. We will focus on unitary-invariant ensembles, where orthogonal polynomials play a key role and whose asymptotic properties can be studied using the Riemann–Hilbert method.

Topics: Unitary-invariant ensembles. Orthogonal polynomials. Determinantal Point Processes. Universality. Riemann-Hilbert problems. Nonlinear steepest descent asymptotic method applied to Orthogonal Polynomials.

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